The Main Group Elements as Materials

The first 36 main group elements exist as well known materials that can be classified as: metals, metalloids and non-metals:

As pure, isolated entities the chemical elements can only undergo phase-change processes:

Simple Binary Compounds (Dielemental Materials)

There are 36 main group elements and there are approximately 650 binary (dielemental) compounds (chemical substances) materials that are derived from the first 36 main group elements.

Compounds can be predicted using a combinatorial matrix (interaction table) of main group elements (a type of Karnaugh map):

The number of binary compounds is approximately 650 because: 36+35+34+... +1 = 666, but helium and neon do not form any known compounds, and some element + element interactions give rise to more than one binary, for example there are several nitrogen-oxygen binaries:

NO, NO2, N2O, N2O4, N2O3 & N2O5
PCl3 & PCl5
IF, IF3, IF5 & IF7
etc.

Of the 45 materials shown in the H to F half-matrix above, three do not exhibit the expected stoichiometry:

* Lithium carbide exists as Li2C2 (lithium acetylide) not Li4C
* Boron carbide exists as B4C not B4C3
* Lithium boride exists as: Li2B3, LiB2 or LiB0.8-1.0, not Li3B

The number of possible CnHm hydrocarbon (and borane, BnHm) homologs and isomers is uncountably huge, here. However, apart from methane, CH4, (and the transient species methylene, CH2, and methine, CH, here) all hydrocarbons contain more than one type of covalent bond: ethane, CH3CH3, has C-C and C-H covalent bonds, for example.

A local, within chemogenesis, definition is:

• Binary materials are substances that exhibit only one type of strong chemical bond.
• Elements are special case binaries where the two elements are identical: H2, etc.

The van Arkel Triangle

Triangles of bonding and material type can be constructed from elements and binary substances. The first was proposed by the Dutchman van Arkel in 1941.

Van Arkel recognised three extreme material and associated bonding types: ionic, metallic and covalent, and he placed these are the corners of an equilateral triangle. He then suggested intermediate species: for example, carbontetrafluoride, CF4, which has C-F bonds that are intermediate between ionic and covalent and are polar covalent. (We will be exploring these intermediate species further, particularly on the next page, here.)

The beauty of the van Arkel analysis is that real chemical species are used to provide hard empirical evidence. The triangle maps material type to theories of chemical structure.

The Ketelaar Triangle

van Arkel's idea was developed by Ketelaar, another Dutchman:

Triangle from the Main Group Interaction Matrix

A triangle of bonding is obtained from main group element interactions, above:

Triangle Rotations & Reflections

It transpires that the idea of a "triangle of bonding" with metallic, ionic and covalent extremes is very rich, and it can be extended in many ways.

The original van Arkel triangle has: covalent at the lower left, ionic at the top and covalent at the lower right, while Ketelaar has: covalent at the lower left, metallic at the top and, ionic at the lower right.

Geometrically, there are six ways to construct triangles through rotation and reflection:

The original van Arkel triangle is CIM, the Ketelaar triangle is CMI, the main group element interaction matrix triangle is IMC,but it is more convenient to use the MIC formulation.

The Jolly Triangle

It is also possible to select different combinations of species to represent metallic, ionic, covalent and intermediate material types. In his 1985 book, William Jolly gives a triangle of bonding with his own selection of species:

Allen's Quantitative Triangle

The Allen triangle of bonding (1992) uses configuration energy (CE): "the average one-electron valence shell energy of the ground-state free atom" as an atomic parameter. CE is used directly to quantify the metal-covalent edge, and the difference in CE is used as a measure of ionic bonding.

The Allen triangle of bonding is restricted to period 3 elements.

Jensen's Quantitative Triangle

William Jensen reviewed the van Arkel-Ketelaar triangle literature in his 1995 paper: J.Chem.Educ. 395-398, 72, 1995. The paper introduces a triangle of bonding quantified in two dimensions using electronegativity data.

The x axis, the metallic-covalent edge, is the average electronegativity of two atoms.

The y axis, ionic character, is the difference in electronegativity.

The Quantified Jensen Triangle of Bonding uses an electronegativity scale introduced by Martynov & Batsanov.

A version of the Jensen triangle using (revised) Pauling electronegativity, is reproduced below for the 481 main group binaries. (Only 31 of the first 36 main group elements have electronegativity data.) This diagram is captured from an Excel spreadsheet, and the original .xls file can be downloaded here.

Norman's Quantitative Triangle

N.C. Norman developed a triangle of bonding that, rather like the Allen version, is quantitative in two dimensions and which (like Jensen) uses electronegativity. However, and very confusingly(!), the Norman Triangle of Bonding uses Allen electronegativity rather than Martynov & Batsanov or revised Pauling electronegativity. And yes, it is the same Allen who uses configuration energy rather than electronegativity.

The astute reader will have noticed how similar the Allen configuration energy (CE) triangle is to the Jensen, Norman and other electronegativity triangles of bonding.

In his 1992 paper, Allen argues that configuration energy, CE, is a fundamental atomic property and is the "missing third dimension to the periodic table", but that electronegativity is simply an "ad hoc" parameter.

More plausibly, it can be argued that Allan's work shows that CE and electronegativity are in some way equivalent; a much more useful idea.

MRL's Quantitative Triangle

My personal take on the van Arkel-Ketelaar triangle is to use a single period, for example: Li to F, and to quantify the ionic-covalent edge in terms of % ionic (or covalent) character using electronegativity data and the Pauling equation:

While the % ionic-covalent character numbers are useful – and they certainly do seem to be a good indication of polarity and reactivity – not too much should be read into them.

Purdue Triangle

From Purdue University chemistry department:

"The bonding between atoms in a solid is determined by a combination of two factors: the magnitude of the electronegativities of the atoms in the solid and the differences between these electronegativities.

"As a result, the bond-type triangle shown in the figure below can be used to predict the classification in which a solid should fall. Compounds with metallic bonds should be metallic solids, those with ionic bonds should be ionic solids, and those with covalent bonds should be either molecular or network covalent solids":

Electrical Conductivity: Metallic Bonding

In his 1995 paper, Jensen pointed out that it is possible to explore the metallic region of the van Arkel-Keteleaar triangle using a simple "probe, battery, buzzer" conductivity test. Materials within the area shown below are "conducting" to this simple test, materials outside are "insulating".

Zintl Phases

Jensen also points out that "Zintl phases", Wikipedia, can be mapped triangle of bonding. Known since the 1930's, "Zintl phases" are formed in liquid ammonia. Zintl phases on the web can be found here.

On this page little has been said about the materials intermediate between:

Metallic and covalent
Metallic and ionic
Covalent and ionic

This topic is developed on the next page, here. There is a software gadget here.

© Mark R. Leach 1999-2008

Queries, Suggestions, Bugs, Errors, Typos...

If you have any:

Queries
Comments
Suggestions
Suggestions for links
Bug, typo or grammatical error reports about this page,

please contact Mark R. Leach, the author, using mrl@meta-synthesis.com

This free, open access web book is an ongoing project and your input is appreciated.